Coulombs Force Solution

Coulombs Force (Triangle with three point charges)
Three charges are placed as shown in the figure below. The magnitude of q1 is 2.00 μC, but its sign and the value of the charge q1 are
not known. Charge q3 is 4.00 μC, and the net force on q3 is entirely in the negative x-direction.
(a) Considering the different possible signs of q1, there are four possible forces diagrams representing the forces that q1 and q2
exert on q3. Sketch these four possible force configurations.
(b) Using the sketches from part (a), and the direction of the net force on q3, deduce the signs of the charges q1 and q2.
(c) Calculate the magnitude of q2.
(d) Determine the magnitude of the net force on q3.
c) Fy must cancel so:
𝐹1𝑜𝑛3𝑦 = 𝐹2𝑜𝑛3𝑦
𝐹1𝑜𝑛3 𝑠𝑖𝑛𝜃1 = 𝐹2𝑜𝑛3 𝑠𝑖𝑛𝜃2
𝑘(2𝜇𝐶)(4𝜇𝐶) 3 𝑘(𝑞2 )(4𝜇𝐶) 4
(0.04𝑚)2 5
(0.03𝑚)2 5
𝑞2 = 0.84𝜇𝐶
d) To determine the magnitude of the net force on q 3, we will need to add the force components in the x-direction from each
of the other charges.
𝐹𝑛𝑒𝑡 = 𝐹1𝑜𝑛3𝑥 + 𝐹2𝑜𝑛3𝑥
= 𝐹1𝑜𝑛3 𝑐𝑜𝑠𝜃 + 𝐹2𝑜𝑛3 𝑐𝑜𝑠𝜃
𝑘(2𝜇𝐶)(4𝜇𝐶) 4 𝑘(0.84𝜇𝐶)(4𝜇𝐶) 3
(0.04𝑚)2 5
= 56.16𝑁